If \( a b=\frac{x(2 b-a)}{b} \) find \( x \) in terms of \( a \) and \( b \)

Solve the equation by following steps: - step0: Solve for \(x\): \(ab=\frac{x\left(2b-a\right)}{b}\) - step1: Rewrite the expression: \(ab=\frac{\left(2b-a\right)x}{b}\) - step2: Swap the sides: \(\frac{\left(2b-a\right)x}{b}=ab\) - step3: Cross multiply: \(\left(2b-a\right)x=bab\) - step4: Simplify the equation: \(\left(2b-a\right)x=b^{2}a\) - step5: Divide both sides: \(\frac{\left(2b-a\right)x}{2b-a}=\frac{b^{2}a}{2b-a}\) - step6: Divide the numbers: \(x=\frac{ab^{2}}{2b-a}\) To find \( x \) in terms of \( a \) and \( b \) from the equation \[ ab = \frac{x(2b - a)}{b}, \] we can rearrange the equation to isolate \( x \). 1. Start by multiplying both sides by \( b \) to eliminate the fraction: \[ ab \cdot b = x(2b - a). \] This simplifies to: \[ ab^2 = x(2b - a). \] 2. Now, solve for \( x \) by dividing both sides by \( (2b - a) \): \[ x = \frac{ab^2}{2b - a}. \] Thus, the value of \( x \) in terms of \( a \) and \( b \) is \[ \boxed{\frac{ab^2}{2b - a}}. \]